DOCSLIB.ORG

Gambler's Fallacy, Hot Hand Belief, and the Time of Patterns

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Gambler's Fallacy, Hot Hand Belief, and the Time of Patterns Judgment and Decision Making, Vol. 5, No. 2, April 2010, pp. 124–132 Gambler’s fallacy, hot hand belief, and the time of patterns Yanlong Sun∗ and Hongbin Wang University of Texas Health Science Center at Houston Abstract The gambler’s fallacy and the hot hand belief have been classified as two exemplars of human misperceptions of random sequential events. This article examines the times of pattern occurrences where a fair or biased coin is tossed repeatedly. We demonstrate that, due to different pattern composition, two different statistics (mean time and waiting time) can arise from the same independent Bernoulli trials. When the coin is fair, the mean time is equal for all patterns of the same length but the waiting time is the longest for streak patterns. When the coin is biased, both mean time and waiting time change more rapidly with the probability of heads for a streak pattern than for a non-streak pattern. These facts might provide a new insight for understanding why people view streak patterns as rare and remarkable. The statistics of waiting time may not justify the prediction by the gambler’s fallacy, but paying attention to streaks in the hot hand belief appears to be meaningful in detecting the changes in the underlying process. Keywords: gambler’s fallacy; hot hand belief; heuristics; mean time; waiting time. 1 Introduction is the representativeness heuristic, which attributes both the gambler’s fallacy and the hot hand belief to a false The gambler’s fallacy and the hot hand belief have been belief of the “law of small numbers” (Gilovich, et al., classified as two exemplars of human misperceptions of 1985; Tversky & Kahneman, 1971). By this account, random sequential events and widely studied in multi- people tend to believe that a local sample should resem- ple disciplines such as psychology, sports, behavioral ble the underlying population and chance is perceived as economics and neuroeconomics (e.g., Camerer, Loewen- “a self-correcting process in which a deviation in one di- stein, & Prelec, 2005; Gilovich, Griffin, & Kahneman, rection induces a deviation in the opposite direction to 2002; Gilovich, Vallone, & Tversky, 1985; Kahneman, restore the equilibrium” (Tversky & Kahneman, 1974, p. 2002; Malkiel, 2003; Rabin, 2002; Rabin & Vayanos, 1125). Thus, in the gambler’s fallacy, a tail is due to re- 2010). Often manifested in more intricate forms, these verse a streak of heads. In the hot hand belief, a streak two phenomena can be demonstrated by independent and of successes may indicate the existence of a hot hand by identically distributed Bernoulli trials. Suppose that a fair which the streak tends to be prolonged (see also Tversky coin with equal probabilities of coming up a head (h) & Gilovich, 1989). and a tail (t) is tossed repeatedly and the first three out- However, the representativeness account has been criti- comes produce three heads (h, h, h). In predicting the cized for its incompleteness and testability (e.g., Ayton & next outcome, one with the gambler’s fallacy would pre- Fischer, 2004; Falk & Konold, 1997; Gigerenzer, 1996; dict (h, h, h, t) — a reversal of the streak. In contrast, Kubovy & Gilden, 1991). Ayton and Fischer (2004) sug- one with the hot hand belief would predict (h, h, h, h) — gest that the gambler’s fallacy arises from the experience a continuation of the streak. of negative recency in sequences of natural events such The fact that people exhibit two opposing expectations as roulette games, but the hot hand belief arises from the upon the same past information — negative recency in experience of positive recency in serial fluctuations in hu- the gambler’s fallacy and positive recency in the hot hand man performance. Similarly, it has been proposed that the belief — has been the center of attention in the research hot hand belief can arise when people evaluate the perfor- on perception of randomness, pattern detection and judg- mance of a mutual fund manager rather than the fluctua- ment of uncertainty (for reviews, see, Ayton & Fischer, tions of the portfolio (Rabin, 2002; Rabin & Vayanos, 2004; Oskarsson, Van Boven, McClelland, & Hastie, 2010), or, the gambler’s luck rather than the outcomes 2009). Among existing theories, a prevailing account of a roulette game (Croson & Sundali, 2005; Sundali & Croson, 2006). Moreover, Burns and Corpus (2004) ∗ Address: Yanlong Sun ([email protected]), or, Hongbin show that subjects assume positive recency for forecast- Wang ([email protected]), School of Health Information Sciences, University of Texas Health Science Center at Houston, 7000 ing scenarios they rated as “nonrandom” and negative re- Fannin St. Suite 600, Houston, TX 77030. cency for scenarios they rated as “random”. Burns (2004) 124 Judgment and Decision Making, Vol. 5, No. 2, April 2010 Gambler’s fallacy hot hand, and timing 125 further argues that the hot hand belief is a fast and fru- It is the goal of this paper to demonstrate a plausible link gal heuristic to detect changes in the shooting accuracy between the statistics of pattern times and people’s per- of basketball players. This argument is consistent with ception of randomness. the finding of “residual nonstationarity” in Sun (2004), in It is important to note that the concept of waiting which it is suggested that the fluctuations in players’ per- time has recently received attention in psychology liter- formance can be obscured by real-time adjustments based ature (Hahn & Warren, 2009; Sun, Tweney, & Wang, on the detection of a hot hand. For example, after making 2010a, 2010b). Hahn and Warren (2009) show that, in several shots in a row, a player might try a more difficult a global sequence of moderate length, streak patterns shot or the opponent players may increase the defense ef- such as (h, h, h, h) have higher “probabilities of nonoc- fort. (For a review on the hot hand study, see Bar-Eli, currence” than (h, h, h, t). Base on this result, they argue Avugos, & Raab, 2006.) that, given people’s limited exposure to the environment Compared to the representativeness account, the alter- (e.g., the number of coin tosses is limited), mispercep- native interpretations distinguish the hot hand belief from tions of randomness such as the gambler’s fallacy might the gambler’s fallacy by deviations from a random pro- actually emerge as apt reflections of these environmen- cess. When the underlying process is truly random (or tal statistics. Sun, Tweney, and Wang (2010a) criticize statistically impossible to tell apart from independent and Hahn and Warren’s interpretation by clarifying the rela- stationary Bernoulli trials), both beliefs are considered tionship between the probability of nonoccurrence and as biases or misperceptions of randomness. In particu- waiting time. In particular, Sun et al. argue that the proba- lar, both beliefs appear to share a common intuition that bility of nonoccurrence is a manifestation of waiting time, streak patterns are “rare” and “remarkable” — a streak which is independent of the length of the global sequence, of heads is unlikely to occur if the coin is fair, or, a bas- and neither statistic would justify the prediction of revert- ketball player is unlikely to make shots in streaks unless ing of a streak by the gambler’s fallacy (also see Sun, et he or she has a hot hand. However, the independence al., 2010b). Notwithstanding the debate, the argument assumption of Bernoulli trials states that, for a fair coin, of treating waiting time as a part of the environmental a streak will occur as often as any other patterns of the statistics appears to be quite plausible. Given that dif- same length in its exact order (i.e., the equiprobability of ferent statistics can arise from the same process of coin “n-grams”, Falk & Konold, 1997, p. 306). Then, what tossing (or basketball shooting), it is likely that they have is so special about streak patterns that people normally been actually experienced by people and have different tend to avoid them and only expect them when they feel effects on people’s perception of randomness. In the fol- “hot”? In the present paper, we show that streak patterns lowing, we examine these statistics in detail and discuss do possess a set of properties that set them apart from their psychological implications. other patterns, and these properties may provide an alter- native explanation for the particular role of streak patterns in people’s perception and judgment of randomness. 2 Mean time, waiting time, and We exemplify by comparing two patterns (h, h, h, t) variance of interarrival times and (h, h, h, h). When a fair coin is tossed repeat- edly, both patterns have the same probability of occur- Let us call the occurrence of a pattern an arrival of the pat- rence in any four successive trials. However, it takes tern when a coin (fair or biased) is tossed repeatedly. We on average 16 tosses to encounter the first occurrence of can define a counting process N (n) , n ≥ 1, where N (n) (h, h, h, t) but 30 tosses to encounter the first occurrence denote the number of arrivals of a pattern by the time n of (h, h, h, h). In other words, streak pattern (h, h, h, h) (i.e., by the nth toss). The process has parameters µ and has been “delayed” for its first occurrence. The expected σ2 as the mean and variance of the time between suc- number of trials required for the first occurrence of a par- cessive arrivals. (A more detailed treatment is provided ticular pattern is a statistical property known as “waiting in the Appendix. The results presented in this paper are time”, which can be different among patterns due to dif- verified by simulations conducted in the R statistics envi- ferent pattern compositions (see Gardner, 1988; Graham, ronment and the scripts are available in this issue of the Knuth, & Patashnik, 1994).
Load more

Recommended publications
  • Read Volume 100 : 25Th October 2015
    Read Volume 100 : 25th October 2015 Forum for Multidisciplinary Thinking !1 Read Volume 100 : 25th October 2015 Contact Page 3: Gamblers, Scientists and the Mysterious Hot Hand By George Johnsonoct Page 8: Daniel Kahneman on Intuition and the Outside View By Elliot Turner Page 13: Metaphors Are Us: War, murder, music, art. We would have none without metaphor By Robert Sapolsky Forum for Multidisciplinary Thinking !2 Read Volume 100 : 25th October 2015 Gamblers, Scientists and the Mysterious Hot Hand By George Johnsonoct 17 October 2015 IN the opening act of Tom Stoppard’s play “Rosencrantz and Guildenstern Are Dead,” the two characters are passing the time by betting on the outcome of a coin toss. Guildenstern retrieves a gold piece from his bag and flips it in the air. “Heads,” Rosencrantz announces as he adds the coin to his growing collection. Guil, as he’s called for short, flips another coin. Heads. And another. Heads again. Seventy-seven heads later, as his satchel becomes emptier and emptier, he wonders: Has there been a breakdown in the laws of probability? Are supernatural forces intervening? Have he and his friend become stuck in time, reliving the same random coin flip again and again? Eighty-five heads, 89… Surely his losing streak is about to end. Psychologists who study how the human mind responds to randomness call this the gambler’s fallacy — the belief that on some cosmic plane a run of bad luck creates an imbalance that must ultimately be corrected, a pressure that must be relieved. After several bad rolls, surely the dice are primed to land in a more advantageous way.
    [Show full text]
  • Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives in Random Bernoulli Sequences
    UNCERTAINTY IN THE HOT HAND FALLACY: DETECTING STREAKY ALTERNATIVES IN RANDOM BERNOULLI SEQUENCES By David M. Ritzwoller Joseph P. Romano Technical Report No. 2019-05 August 2019 Department of Statistics STANFORD UNIVERSITY Stanford, California 94305-4065 UNCERTAINTY IN THE HOT HAND FALLACY: DETECTING STREAKY ALTERNATIVES IN RANDOM BERNOULLI SEQUENCES By David M. Ritzwoller Joseph P. Romano Stanford University Technical Report No. 2019-05 August 2019 Department of Statistics STANFORD UNIVERSITY Stanford, California 94305-4065 http://statistics.stanford.edu Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives in Random Bernoulli Sequences David M. Ritzwoller, Stanford University∗ Joseph P. Romano, Stanford University August 22, 2019 Abstract We study a class of tests of the randomness of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks as overly representative of positive dependence—the hot hand fallacy. In particular, we study tests of randomness (i.e., that tri- als are i.i.d.) based on test statistics that compare the proportion of successes that directly follow k consecutive successes with either the overall proportion of successes or the pro- portion of successes that directly follow k consecutive failures. We derive the asymptotic distributions of these test statistics and their permutation distributions under randomness and under general models of streakiness, which allows us to evaluate their local asymp- totic power. The results are applied to revisit tests of the hot hand fallacy implemented on data from a basketball shooting experiment, whose conclusions are disputed by Gilovich, Vallone, and Tversky (1985) and Miller and Sanjurjo (2018a). We establish that the tests are insufficiently powered to distinguish randomness from alternatives consistent with the variation in NBA shooting percentages.
    [Show full text]
  • Surprised by the Gambler's and Hot Hand Fallacies?
    Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers Joshua B. Miller and Adam Sanjurjo ∗yz September 24, 2015 Abstract We find a subtle but substantial bias in a standard measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The mechanism is a form of selection bias, which leads the empirical probability (i.e. relative frequency) to underestimate the true probability of a given outcome, when conditioning on prior outcomes of the same kind. The biased measure has been used prominently in the literature that investigates incorrect beliefs in sequential decision making|most notably the Gambler's Fallacy and the Hot Hand Fallacy. Upon correcting for the bias, the conclusions of some prominent studies in the literature are reversed. The bias also provides a structural explanation of why the belief in the law of small numbers persists, as repeated experience with finite sequences can only reinforce these beliefs, on average. JEL Classification Numbers: C12; C14; C18;C19; C91; D03; G02. Keywords: Law of Small Numbers; Alternation Bias; Negative Recency Bias; Gambler's Fal- lacy; Hot Hand Fallacy; Hot Hand Effect; Sequential Decision Making; Sequential Data; Selection Bias; Finite Sample Bias; Small Sample Bias. ∗Miller: Department of Decision Sciences and IGIER, Bocconi University, Sanjurjo: Fundamentos del An´alisisEcon´omico, Universidad de Alicante. Financial support from the Department of Decision Sciences at Bocconi University, and the Spanish Ministry of Economics and Competitiveness under project ECO2012-34928 is gratefully acknowledged. yBoth authors contributed equally, with names listed in alphabetical order.
    [Show full text]
  • Infographic I.10
    The Digital Health Revolution: Leaving No One Behind The global AI in healthcare market is growing fast, with an expected increase from $4.9 billion in 2020 to $45.2 billion by 2026. There are new solutions introduced every day that address all areas: from clinical care and diagnosis, to remote patient monitoring to EHR support, and beyond. But, AI is still relatively new to the industry, and it can be difficult to determine which solutions can actually make a difference in care delivery and business operations. 59 Jan 2021 % of Americans believe returning Jan-June 2019 to pre-coronavirus life poses a risk to health and well being. 11 41 % % ...expect it will take at least 6 The pandemic has greatly increased the 65 months before things get number of US adults reporting depression % back to normal (updated April and/or anxiety.5 2021).4 Up to of consumers now interested in telehealth going forward. $250B 76 57% of providers view telehealth more of current US healthcare spend % favorably than they did before COVID-19.7 could potentially be virtualized.6 The dramatic increase in of Medicare primary care visits the conducted through 90% $3.5T telehealth has shown longevity, with rates in annual U.S. health expenditures are for people with chronic and mental health conditions. since April 2020 0.1 43.5 leveling off % % Most of these can be prevented by simple around 30%.8 lifestyle changes and regular health screenings9 Feb. 2020 Apr. 2020 OCCAM’S RAZOR • CONJUNCTION FALLACY • DELMORE EFFECT • LAW OF TRIVIALITY • COGNITIVE FLUENCY • BELIEF BIAS • INFORMATION BIAS Digital health ecosystems are transforming• AMBIGUITY BIAS • STATUS medicineQUO BIAS • SOCIAL COMPARISONfrom BIASa rea• DECOYctive EFFECT • REACTANCEdiscipline, • REVERSE PSYCHOLOGY • SYSTEM JUSTIFICATION • BACKFIRE EFFECT • ENDOWMENT EFFECT • PROCESSING DIFFICULTY EFFECT • PSEUDOCERTAINTY EFFECT • DISPOSITION becoming precise, preventive,EFFECT • ZERO-RISK personalized, BIAS • UNIT BIAS • IKEA EFFECT and • LOSS AVERSION participatory.
    [Show full text]
  • Illusionary Pattern Detection in Habitual Gamblers
    Article Illusionary pattern detection in habitual gamblers WILKE, Andreas, et al. Abstract Does problem gambling arise from an illusion that patterns exist where there are none? Our prior research suggested that “hot hand,” a tendency to perceive illusory streaks in sequences, may be a human universal, tied to an evolutionary history of foraging for clumpy resources. Like other evolved propensities, this tendency might be expressed more stongly in some people than others, leading them to see luck where others see only chance. If the desire to gamble is enhanced by illusory pattern detection, such individual differences could be predictive of gambling risk. While previous research has suggested a potential link between cognitive strategies and propensity to gamble, no prior study has directly measured gamblers' cognitive strategies using behavioral choice tasks, and linked them to risk taking or gambling propensities. Using a computerized sequential decision-making paradigm that directly measured subjects' predictions of sequences, we found evidence that subjects who have a greater tendency to gamble also have a higher tendency to perceive illusionary patterns, as measured by their preferences for a random [...] Reference WILKE, Andreas, et al. Illusionary pattern detection in habitual gamblers. Evolution and Human Behavior, 2014, vol. 35, no. 4, p. 291-297 DOI : 10.1016/j.evolhumbehav.2014.02.010 Available at: http://archive-ouverte.unige.ch/unige:76433 Disclaimer: layout of this document may differ from the published version. 1 / 1 Evolution and Human Behavior 35 (2014) 291–297 Contents lists available at ScienceDirect Evolution and Human Behavior journal homepage: www.ehbonline.org Original Article Illusionary pattern detection in habitual gamblers☆ Andreas Wilke a,⁎, Benjamin Scheibehenne b, Wolfgang Gaissmaier c, Paige McCanney a, H.
    [Show full text]
  • The Gambler's and Hot-Hand Fallacies: Theory and Applications
    Review of Economic Studies (2010) 77, 730–778 0034-6527/10/00411011$02.00 © 2009 The Review of Economic Studies Limited doi: 10.1111/j.1467-937X.2009.00582.x The Gambler’s and Hot-Hand Fallacies: Theory and Applications MATTHEW RABIN University of California, Berkeley and DIMITRI VAYANOS London School of Economics, CEPR and NBER First version received September 2007; final version accepted May 2009 (Eds.) We develop a model of the gambler’s fallacy—the mistaken belief that random sequences should exhibit systematic reversals. We show that an individual who holds this belief and observes a sequence of signals can exaggerate the magnitude of changes in an underlying state but underestimate their duration. When the state is constant, and so signals are i.i.d., the individual can predict that long streaks of similar signals will continue—a hot-hand fallacy. When signals are serially correlated, the individual typically under-reacts to short streaks, over-reacts to longer ones, and under-reacts to very long ones. Our model has implications for a number of puzzles in finance, e.g. the active-fund and fund-flow puzzles, and the presence of momentum and reversal in asset returns. 1. INTRODUCTION Many people fall under the spell of the “gambler’s fallacy”, expecting outcomes in random sequences to exhibit systematic reversals. When observing flips of a fair coin, for example, people believe that a streak of heads makes it more likely that the next flip will be a tail. The gambler’s fallacy is commonly interpreted as deriving from a fallacious belief in the “law of small numbers” or “local representativeness”: people believe that a small sample should resem- ble closely the underlying population, and hence believe that heads and tails should balance even in small samples.
    [Show full text]
  • The Hot Hand Phenomenon in Basketball Revisited
    Clemson University TigerPrints All Theses Theses 8-2018 The otH Hand Phenomenon in Basketball Revisited Alexander T. Dahlstrom Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_theses Recommended Citation Dahlstrom, Alexander T., "The otH Hand Phenomenon in Basketball Revisited" (2018). All Theses. 2952. https://tigerprints.clemson.edu/all_theses/2952 This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact [email protected]. THE HOT HAND PHENOMENON IN BASKETBALL REVISITED A Thesis Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Master of Arts Economics by Alexander T. Dahlstrom August 2018 Accepted by: Dr. Raymond Sauer, Committee Chair Dr. Scott Templeton Dr. Robert Fleck ABSTRACT The focus of this paper is to summarize the economic literature of the hot hand phenomenon in basketball while adding in another study of my own. By using recent NBA statistical data, I will show the advancement and evolution of this widely held public belief that a certain number of makes or misses can alter the chances of the next attempt’s success or failure. I start by recreating part of Gilovich, Valone, and Tversky’s (1985) experiments with a larger set of data and finish by introducing Miller and Sanjurjo’s fix to their method’s biases(2015). The major finding is when a three and an eight percentage point correction for the bias from Miller and Sanjurjo’s calculations are applied to my data set as well as many other studies, that a hot hand effect starts to surface more frequently.
    [Show full text]
  • The Hot Hand and Psychological Momentum As Adaptive Beliefs in Sport Barack Little
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2014 The Hot Hand and Psychological Momentum as Adaptive Beliefs in Sport Barack Little Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF EDUCATION THE HOT HAND AND PSYCHOLOGICAL MOMENTUM AS ADAPTIVE BELIEFS IN SPORT By BARACK LITTLE A Thesis submitted to the Department of Educational Psychology and Learning Systems in partial fulfillment of the requirements for the degree of Master of Science Degree Awarded: Summer Semester, 2014 BaRack Little defended this thesis on July 14, 2014. The members of the supervisory committee were: Gershon Tenenbaum Professor Directing Thesis Beth Phillips Committee Member Insu Paek Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the thesis has been approved in accordance with university requirements. ii To spirituality, positivity, genuineness, challenging life’s norms, and last but not least, my mother: The things that have motivated me and brought me this far. iii ACKNOWLEDGMENTS First and foremost, I would like to thank my mother, LuRoyal, for all of the love and support—both motivationally and financially—that you have given me throughout this academic journey. You have raised me to be respectful, genuine, and strong, but most importantly, you have raised me to believe that anything is attainable in life. For that I owe you the utmost gratitude. To the team and my Birch brothers, you have always been there for me and never let me stop working! You all truly understood what it took to get here, and I appreciate every bit of advice and support.
    [Show full text]
  • Preregistration: a Pragmatic Tool to Reduce Bias and Calibrate Confidence in Scientific Research
    PERSPECTIVE Preregistration: A pragmatic tool to reduce bias and calibrate confidence in scientific research Tom E. Hardwicke* & Eric-Jan Wagenmakers# Department of Psychology, University of Amsterdam Scientific research is performed by fallible humans. Degrees of freedom in the construction and selection of evidence and hypotheses grant scientists considerable latitude to obtain study outcomes that align more with their preferences than is warranted. This creates a risk of bias and can lead to scientists fooling themselves and fooling others. Preregistration involves archiving study information (e.g., hypotheses, methods, and analyses) in a public registry before data are inspected. This offers two potential benefits: (1) reduce bias by ensuring that research decisions are made independently of study outcomes; and (2) calibrate confidence in research by transparently communicating information about a study’s risk of bias. In this article, we briefly review the historical evolution of preregistration in medicine, psychology, and other domains, clarify its pragmatic functions, discuss relevant meta-research, and provide recommendations for scientists and journal editors. * [email protected] ORCID: 0000-0001-9485-4952 # [email protected] ORCID: 0000-0003-1596-1034 “The mind lingers with pleasure upon the facts that fall happily into the embrace of the theory...There springs up...an unconscious pressing of the theory to make it fit the facts, and a pressing of the facts to make them fit the theory.” — Chamberlin (1890/1965)1 “We are human after all.” — Daft Punk (2005)2 1. Introduction Science is a human endeavour and humans are fallible. Scientists’ cognitive limitations and self-interested motivations can infuse bias into the research process, undermining the production of reliable knowledge (Box 1)3–6.
    [Show full text]
  • Thoughts on the Hot-Hand Debate in Basketball
    BEHAVIORAL INSIGHTS • APR 2019 Thoughts on the Hot-Hand Debate in Basketball AUTHORS “In science, convictions have no rights of citizenship.” – Nietzsche The debate on the “hot hand” in basketball has gone on for decades. On one side, most players, coaches and fans are adamant that hot hands exist, with players experiencing winning streaks that cannot be explained by chance. On the other side, since the seminal paper of Gilovich, Vallone and Tversky (henceforth GVT) in 1985, most academic research has been unable to find statistical evidence to support the idea of the hot hand. The stark contrast between the two sides has made Emmanuel Roman Chief Executive Officer the belief in the hot hand in basketball one of the most massive and widespread cognitive illusions Managing Director cited in the literature on heuristics and biases (see, for example, Kahneman 2011). Although for decades the dust seemed to have settled on the issue, at least for the academic community, a recent paper by Miller and Sanjurjo (2018) revived the debate by pointing out a finite sample bias previously overlooked by GVT and other researchers.1 After correcting for the bias, the authors claim that the data used by GVT actually provided evidence for the hot hand in basketball. Jamil Baz Managing Director We find this paper fascinating in many ways. It identifies a subtle but substantial bias underlying a Client Solutions and Analytics standard measure of conditional dependence of random outcomes on past outcomes in sequential data, and therefore has wide implications for future research in finance. In addition, the overlooked bias itself can be interpreted as a result of the researchers’ belief in the law of small numbers.
    [Show full text]
  • The Effects of Heuristics and Apophenia on Probabilistic Choice Zack W
    RESEARCH ARTICLE ADVANCES IN COGNITIVE PSYCHOLOGY The Effects of Heuristics and Apophenia on Probabilistic Choice Zack W. Ellerby and Richard J. Tunney School of Psychology, University of Nottingham, Nottingham, United Kingdom ABSTRACT Given a repeated choice between two or more options with independent and identically distrib- uted reward probabilities, overall pay-offs can be maximized by the exclusive selection of the op- tion with the greatest likelihood of reward. The tendency to match response proportions to re- ward contingencies is suboptimal. Nevertheless, this behaviour is well documented. A number of explanatory accounts have been proposed for probability matching. These include failed pattern matching, driven by apophenia, and a heuristic-driven response that can be overruled with suf- ficient deliberation. We report two experiments that were designed to test the relative effects on choice behaviour of both an intuitive versus strategic approach to the task and belief that there was a predictable pattern in the reward sequence, through a combination of both direct experi- mental manipulation and post-experimental self-report. Mediation analysis was used to model the pathways of effects. Neither of two attempted experimental manipulations of apophenia, nor self-reported levels of apophenia, had a significant effect on proportions of maximizing choices. However, the use of strategy over intuition proved a consistent predictor of maximizing, across KEYWORDS all experimental conditions. A parallel analysis was conducted to assess the effect of controlling for individual variance in perceptions of reward contingencies. Although this analysis suggested probability matching, that apophenia did increase probability matching in the standard task preparation, this effect was apophenia, heuristics, found to result from an unforeseen relationship between self-reported apophenia and perceived judgement reward probabilities.
    [Show full text]
  • EXPLORING the HOT HAND PHENOMENON a Thesis Submitted
    DETECTING STRUCTURE IN ACTIVITY SEQUENCES: EXPLORING THE HOT HAND PHENOMENON A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By TALERI HAMMACK B.S., University of Idaho, 2012 2015 Wright State University WRIGHT STATE UNIVERSITY GRADUATE SCHOOL August 20, 2015 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Taleri Hammack ENTITLED Detecting Structure in Activity Sequences: Exploring the Hot Hand Phenomenon BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Masters of Science . ____________________________ John Flach, Ph.D. Thesis Director ___________________________ Scott Watamaniuk, Ph.D. Graduate Program Director ___________________________ Debra Steele-Johnson, Ph.D. Chair, Department of Psychology Committee on Final Examination _________________________________ John Flach, Ph.D. _________________________________ Kevin Bennett, Ph.D. _________________________________ Joseph Houpt, Ph.D. _________________________________ Robert E. W. Fyffe, Ph.D. Vice President for Research and Dean of the Graduate School ABSTRACT Hammack, Taleri Lynn. M.S. Human Factors and Industrial/Organizational Psychology, Department of Psychology, Wright State University, 2015. Detecting Structure in Activity Sequences: Exploring the Hot Hand Phenomenon. Can humans discriminate whether strings of events (e.g., shooting success in basketball) were generated by a random or constrained process (e.g., hot and cold streaks)? Conventional wisdom suggests that humans are not good at this discrimination. Following from Cooper, Hammack, Lemasters, and Flach (2014), a series of Monte Carlo simulations and an empirical experiment examined the abilities of both humans and statistical tests (Wald-Wolfowitz Runs Test and 1/f) to detect specific constraints that are representative of plausible factors that might influence the performance of athletes (e.g., learning, non-stationary task constraints).
    [Show full text]